The commercial success of an Asynchronous Transfer Mode (ATM) switch hinges on whether the switch is "growable"--meaning that the switching capacity of the switch may be expanded to handle an increase in bandwidth. For example, U.S. Pat. No. 5,256,265 discloses an architecture for an ATM switch which may grow (expand) from an 8.times.8 packet switch to a 32.times.32 packet switch, as shown in FIG. 1. One drawback of such an architecture is that when the capacity of the switch is expanded, the required concentration access speed increases proportionately. Another drawback is that the bandwidth data rate at the output of an expansion unit 404 becomes k times the input bandwidth data rate of the switch, where k is the number of 8.times.8 packet switch modules employed at the output of the switch. For example, for an nxn switch, then the expansion bandwidth is kxnxR, where R is the input bandwidth of each line and is typically 2.4 gigabits/sec. Since k is proportional to the size of an ATM switch, i.e., k is proportional to n, then it can be appreciated that the bandwidth of the interconnection between the expansion unit 404 and associated concentrators 101 grows as the square of the size of the switch and, therefore, becomes unwieldy to implement when the size of the ATM switch is increased.